{"id":"https://openalex.org/W3090971396","doi":"https://doi.org/10.3233/faia200221","title":"Mean Field Theory for Deep Dropout Networks: Digging up Gradient Backpropagation Deeply","display_name":"Mean Field Theory for Deep Dropout Networks: Digging up Gradient Backpropagation Deeply","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3090971396","doi":"https://doi.org/10.3233/faia200221","mag":"3090971396"},"language":"en","primary_location":{"id":"doi:10.3233/faia200221","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia200221","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.3233/faia200221","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Huang Wei","orcid":null},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Huang Wei","raw_affiliation_strings":["University of Science and Technology of China, Hefei, China"],"affiliations":[{"raw_affiliation_string":"University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073709711","display_name":"Richard Yi Da Xu","orcid":"https://orcid.org/0000-0003-2080-4762"},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Xu Richard Yi Da","raw_affiliation_strings":["University of Technology Sydney, Sydney, Australia"],"affiliations":[{"raw_affiliation_string":"University of Technology Sydney, Sydney, Australia","institution_ids":["https://openalex.org/I114017466"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080452660","display_name":"Weitao Du","orcid":"https://orcid.org/0000-0001-7643-4671"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Du Weitao","raw_affiliation_strings":["Northwestern University, Evanston, United States"],"affiliations":[{"raw_affiliation_string":"Northwestern University, Evanston, United States","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065071752","display_name":"Yutian Zeng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zeng Yutian","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5041580755","display_name":"Yunce Zhao","orcid":"https://orcid.org/0009-0000-2290-2046"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhao Yunce","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I126520041"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17414441,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1215","last_page":"1222"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.9821000099182129,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12676","display_name":"Machine Learning and ELM","score":0.9764000177383423,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/backpropagation","display_name":"Backpropagation","score":0.8886052370071411},{"id":"https://openalex.org/keywords/dropout","display_name":"Dropout (neural networks)","score":0.6837555170059204},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6008014678955078},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5659873485565186},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48061221837997437},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.45796090364456177},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3984341025352478},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38158971071243286},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.2200516164302826}],"concepts":[{"id":"https://openalex.org/C155032097","wikidata":"https://www.wikidata.org/wiki/Q798503","display_name":"Backpropagation","level":3,"score":0.8886052370071411},{"id":"https://openalex.org/C2776145597","wikidata":"https://www.wikidata.org/wiki/Q25339462","display_name":"Dropout (neural networks)","level":2,"score":0.6837555170059204},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6008014678955078},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5659873485565186},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48061221837997437},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.45796090364456177},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3984341025352478},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38158971071243286},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2200516164302826}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3233/faia200221","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia200221","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},{"id":"mag:3090971396","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1912.09132.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"doi:10.3233/faia200221","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia200221","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2894173309","https://openalex.org/W2115605526","https://openalex.org/W4387932263","https://openalex.org/W2098962763","https://openalex.org/W3093883775","https://openalex.org/W1539246760","https://openalex.org/W2786746258","https://openalex.org/W2371065793","https://openalex.org/W2157746493","https://openalex.org/W4225893763"],"abstract_inverted_index":{"In":[0],"recent":[1,43],"years,":[2],"the":[3,11,48,58,65,75,81,95,113,158,175,182,192,203,229],"mean":[4,53,187],"field":[5,54],"theory":[6,25,55],"has":[7,17,26,45],"been":[8,27],"applied":[9,28],"to":[10,29,122,126],"study":[12,181],"of":[13,22,50,60,68,145,170,188,191,198,214],"neural":[14,31,104],"networks":[15,105,141,210],"and":[16,39,71,142,167,186,194,218,220],"achieved":[18],"a":[19,109,118,143,164,168,212,222],"great":[20],"deal":[21],"success.":[23],"The":[24,52],"various":[30],"network":[32],"structures,":[33],"including":[34],"CNNs,":[35],"RNNs,":[36],"Residual":[37],"networks,":[38],"Batch":[40],"normalization.":[41],"Inevitably,":[42],"work":[44],"also":[46],"covered":[47],"use":[49],"dropout.":[51],"shows":[56],"that":[57,63,85,157,227],"existence":[59],"depth":[61,67,177],"scales":[62],"limit":[64],"maximum":[66,204],"signal":[69],"propagation":[70],"gradient":[72,76,82,193],"backpropagation.":[73,99,129],"However,":[74],"backpropagation":[77],"is":[78,101],"derived":[79],"under":[80],"independence":[83],"assumption":[84],"weights":[86,115],"used":[87,97,116],"during":[88],"feed":[89],"forward":[90],"are":[91,106,172],"drawn":[92],"independently":[93],"from":[94],"ones":[96],"in":[98,108,117],"This":[100],"not":[102],"how":[103],"trained":[107],"real":[110],"setting.":[111],"Instead,":[112],"same":[114,176],"feed-forward":[119],"step":[120],"needs":[121],"be":[123],"carried":[124],"over":[125],"its":[127],"corresponding":[128],"Using":[130],"this":[131],"realistic":[132],"condition,":[133],"we":[134,180,201],"perform":[135],"theoretical":[136],"computation":[137],"on":[138,147],"linear":[139],"dropout":[140,148,209],"series":[144,213],"experiments":[146,215],"networks.":[149],"Our":[150],"empirical":[151,225],"results":[152],"show":[153],"an":[154,196],"interesting":[155],"phenomenon":[156],"length":[159,206,231],"gradients":[160],"can":[161],"backpropagate":[162],"for":[163,207],"single":[165],"input":[166],"pair":[169],"inputs":[171],"governed":[173],"by":[174],"scale.":[178],"Besides,":[179],"relationship":[183],"between":[184],"variance":[185],"statistical":[189],"metrics":[190],"shown":[195],"emergence":[197],"universality.":[199],"Finally,":[200],"investigate":[202],"trainable":[205,230],"deep":[208],"through":[211],"using":[216],"MNIST":[217],"CIFAR10":[219],"provide":[221],"more":[223],"precise":[224],"formula":[226],"describes":[228],"than":[232],"original":[233],"work.":[234]},"counts_by_year":[],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2020-10-08T00:00:00"}